Objective C is a superset of the C language, therefore you can use "math.h".
The function that computes the natural logarithm from "math.h" is double log(double x);
EDIT
Since you want the difficulty to increase as a function of time, you would pass the time as the argument to log(double x)
. How you would use that to calculate and change the "difficulty" is an entirely different question.
If you want to change the shape of the curve, either multiply the expression by a constant, as in 2*log(x)
or multiply the parameter by a constant, as in log(2*x)
. You will have to look at the individual curves to see what will work best for your specific application.